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Anybody who can help me with a differential?

The book mentions that a differential is 111pi. However, the differential I worked out after 30 minutes solving was 1.7pi. The question was:

Estimate the change in the volume of a cylinder, if the radius increases from 30 to 30.2, and the height decreases from 10 to 9.99. (HINT: V=pi r^2 h)

3 Answers

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  • 1 decade ago
    Favorite Answer

    dV

    = d (pi r^2 h)

    = pi d (r^2 h)

    = pi (2rh dr + r^2 dh)

    = pi [ 2*30*10*(0.2) + 30^2 *(-0.01) ]

    = pi [ 120 - 9 ]

    = 111 pi

  • 1 decade ago

    Vo= pi*30^2*10=9000pi

    V= pi*30.2^2*9.99=9111.3pi

    V-Vo= 111.3pi

  • gebobs
    Lv 6
    1 decade ago

    Solve the equation for both.

    V1 = 10*30²π = 9000π

    V2 = 9.9*30.2²π = 9111π

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